These are the weakest of any, although there are exceptions. Zabuza, not even being graduated yet, slaughtered more than a hundred of that year's graduates. Gaara, as well, could kill any Chuunin and Jounin that tried to assassinate him at the age of six. Generally are being taught basic techniques, like Clones, Kawarimi, etc..
Academy student graduates. They demonstrated the ability to pass and are proficient at basic techniques, such as Bunshin no Jutsu. They are assigned to a Jounin, usually three genin to each Jounin. They are then allowed to do mundane and boring tasks, such as weeding, walking a rich man's dogs or finding a fat, rich woman's cat who had reason to flee it's master.
After participating in the Chuunin exam, a genin's intellect and strength are judged by the Kages and Lords that preside as judges. They are now qualified to lead a group of genins during extracurricular activities, such as the village being under attack. They are also sent out on solo or group missions. They mostly travel in groups of four on missions.
A Jounin that specializes in a specific area of expertise. Morino Ibiki, for example, is head of the Konoha's Interrogation Unit, which is basically torture. Anko is a Special Jounin because of her familiarity with the recent Village of Sound, which Konoha has next to no information about. ANBU teams, which serve as police and assassination squads, are also Special Jounins.
Chuunins who have shown extraordinary amounts of strength and intelligence are promoted to Jounin. This is a high ranking, and one is sent on more difficult missions than Chuunins, usually involving assassination or theft, or in some cases, information gathering. Jounins are also believed to be mature enough to handle a squad of genins and to train them.
A specific devision of ninjas designed much like the royal guard of the Hokage. This group performs assasinations, escorts, and act as body guards as well for the current Hokage. Kakashi was once an ANBU member himself.
Ninjas who have abandoned their village and gone on the run. As a result, they are marked for death by their village's hunter-nins, who will hunt them ceaselessly until they either die or get their target..
The ultimate warrior and leader of a particular village, in other words: the title of referring to the strongest in the village. What they say usually goes. Their power is only rivaled by other Kages. (examples: Hokage, Kazekage, etc)